Abstract
For problems SAT and MAX SAT, local search algorithms are widely acknowledged as one of the most effective approaches. Most of the local search algorithms are based on the 1-flip neighborhood, which is the set of solutions obtainable by flipping the truth assignment of one variable. In this paper, we consider r-flip neighborhoods for r ≥ 2, and propose, for r = 2, 3, new implementations that reduce the number of candidates in the neighborhood without sacrificing the solution quality. For 2-flip (resp., 3-flip) neighborhood, we show that its expected size is O(n + m) (resp., O(m + t2n)), which is usually much smaller than the original size O(n2) (resp., O(n3)), where n is the number of variables, m is the number of clauses and t is the maximum number of appearances of one variable. Computational results tell that these estimates by the expectation well represent the real performance.
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Yagiura, M., Ibaraki, T. Analyses on the 2 and 3-Flip Neighborhoods for the MAX SAT. Journal of Combinatorial Optimization 3, 95–114 (1999). https://doi.org/10.1023/A:1009873324187
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DOI: https://doi.org/10.1023/A:1009873324187